According to Mike Trudell of Spectrum SportsNet, Rondo was diagnosed with a non-displaced plate avulsion fracture of the right ring finger. His status is considered day-to-day.
Trudell noted forward Anthony Davis (bruised buttocks) will also miss Monday's contest, while LeBron James and Avery Bradley are available despite dealing with flu-like symptoms.
Rondo is one of the few holdovers from last season's squad, having signed a two-year, $5.2 million deal to return to Los Angeles.
With James operating more at point guard, Rondo has been shuffled to the bench. He's averaging 7.6 points and 5.4 assists through 27 appearances. His 21.6 minutes per game are on pace to be a career low.
The 33-year-old has picked up a few minor injuries in 2019-20. He was out for the first nine games because of a mild calf strain and missed a pair of games in December with a hamstring strain. Then he strained his right ring finger in the Lakers' 125-110 win over the Oklahoma City Thunder on Jan. 11.
In addition to the Lakers minimizing Rondo's role slightly, Alex Caruso has emerged as a capable backup for limited stretches. The third-year guard is averaging 5.8 points and 1.7 assists.
Although Los Angeles will miss Rondo's presence in the backcourt, his injury shouldn't significantly disrupt things for head coach Frank Vogel.